A known method of measuring range and range rate of a target consists of providing apparatus for producing a continuous wave carrier frequency modulated by a repeatable waveform such as a triangle, a sawtooth, a sine wave, or the like which signal is radiated to the target of interest. The signal is returned from the target to the apparatus and mixed with the transmitted signal to produce a beat frequency.
For a triangular waveform, the beat frequency f.sub.B is given by the formula: ##EQU1##
The symbols in formula (1) have the following meaning and in one exemplary embodiment the following values:
.DELTA.F = modulation frequency deviation = 25 MHz; PA1 F.sub.m = 1/T = modulation rate = 3 KHz; PA1 R = range of target from the apparatus = 0 to 100 meters; PA1 F.sub.0 = carrier frequency = 10.575 GHz; PA1 R = range rate or velocity of target = 0-76.5 kilometers/hour; PA1 C = speed of light.
The plus sign in formula (1) is associated with the modulation upsweep and the minus sign with modulation downsweep. By rearranging formula (1) both range and range rate of a target may be determined as follows: ##EQU2##
Where f.sub.B avg is the measured beat frequency as averaged over upsweep and downsweep of the modulation cycle.
Likewise: ##EQU3##
Where f.sub.d = f.sub.B avg - formula (1) using only the plus sign.
In theory formula (3) may be used to determine range rate directly. In practice, however, given the parameters of the exemplary system, the determination of the frequencies involved in formula (3) is difficult. Another method to determine range rate is to determine range by formula 2 and then differentiate with respect to time, i.e., ##EQU4##
From formula (2) it will be noted that a determination of R requires a determination of average beat frequency. One method of determining beat frequency is to count the number, N, cycles of the beat frequency over one modulation cycle and multiply by f.sub.m. As N can only be an integer the determined frequency will only be in multiples of f.sub.m. Thus the determined range will only be in multiples of f.sub.m. For parameters of the exemplary system, the computed range will be in increments of 1.5 meters which is known as range granularity. Such granularity will also appear in the range rate measurement of formula 4 and is not acceptable in some applications.
Further, at each turnaround point of the modulation waveform such as at the junction of an unsweep and a downsweep portion of a triangular waveform, the beat frequency is indeterminant. In the case of a triangular waveform, the beat frequency is symmetrical about each turnaround point. Additionally, if the target has any velocity component relative to the measuring apparatus the symmetrical beat frequency will cross or not cross its average value at successive turnaround points at a rate dependent on the velocity of the target. D. G. C. Luck, "Frequency Modulated Radar" McGraw-Hill, Inc., New York, 1949) in FIG. IV-II (h), pg. 106 shows that the indicated beat note frequency, as determined by counting its cycles, changes by one for each .lambda./4 of target motion, where .lambda. is the wavelength of the carrier frequency, f.sub.0, for a unit with the exemplary parameters and with f.sub.0 = 10.575 GHz .lambda./4 = 0.71 centimeters. Thus for each movement of the target of approximately 0.71 centimeters the beat frequency determined by counting beat frequency cycles changes by one, alternately increasing and decreasing. This change in the number of cycles is manifested as crossing and non-crossing of the beat frequency about its average value at the modulation turnaround points as mentioned above.
The range may also be determined by determining the time to complete one cycle of beat frequency which will be as accurate as the clock used to determine the time. However, to determine range and therefore range rate which sufficient accuracy in some applications, requires a clock with such precision as to make it prohibitively expensive. Thus formula (4) does not provide satisfactory determination of range rate given the exemplary parameters of interest.
A second method of determining range rate involves utilizing a waveform which is continuous wave frequency modulated interspersed with a waveform which is not modulated. The nonmodulated waveform is used to determine range rate in a known manner. Generation of such a dual waveform requires relatively complex and costly equipment.